Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:59:57.905Z Has data issue: false hasContentIssue false
  • English
  • Français

Slices of motivic Landweber spectra

Published online by Cambridge University Press:  19 November 2010

Markus Spitzweck
Markus Spitzweck
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Germany, and Mathematical Department, University Oslo, Norway, Markus.Spitzweck@mathematik.uni-regensburg.de, markussp@math.uio.no
Get access

Abstract

In this paper we show that a conjecture of Voevodsky about the slices of the motivic cobordism spectrum implies a statement about the slices of motivic Landweber spectra. Over perfect fields these slices are given by the coefficients of the corresponding topological Landweber spectrum and the motivic Eilenberg MacLane spectrum. We also prove a cohomological version of Landweber exactness which applies to the compact objects of the stable motivic homotopy category.

Keywords

motivic Landweber spectraslice filtrationalgebraic cobordismspectrum
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 1 , February 2012 , pp. 103 - 117
Copyright
Copyright © ISOPP 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Christensen, J. Daniel and Strickland, Neil P.. Phantom maps and homology theories. Topology 37(2) :339–364, 1998.CrossRefGoogle Scholar
2.Elmendorf, A. D., Kriz, I., Mandell, M. A., and May, J. P.. Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, American Mathematical Society, Providence, RI, 1997.Google Scholar
3.Hovey, Mark and Strickland, Neil P.. Morava K-theories and localisation. Mem. Amer. Math. Soc. 139(666):viii+100, 1999.Google Scholar
4.Krause, Henning. Localization theory for triangulated categories. arXiv:0806.1324.Google Scholar
5.Levine, Marc. The homotopy coniveau tower. J. Topol. 1(1):217–267, 2008.CrossRefGoogle Scholar
6.Lurie, Jacob. Higher topos theory, Annals of Mathematics Studies 170. Princeton University Press, Princeton, NJ, 2009.Google Scholar
7.Naumann, Niko, Spitzweck, Markus, and Østvær, Paul Arne. Motivic Landweber exactness. Doc. Math. 14:551–593, 2009.CrossRefGoogle Scholar
8.Neeman, Amnon. The Grothendieck duality theorem via Bousfield's techniques and Brown representability. J. Amer. Math. Soc. 9(1):205–236, 1996.CrossRefGoogle Scholar
9.Panin, Ivan, Pimenov, Konstantin, and Röndigs, Oliver. A universality theorem for Voevodsky's algebraic cobordism spectrum. Homology, Homotopy Appl. 10(2):211–226, 2008.CrossRefGoogle Scholar
10.Pelaez, Pablo. Multiplicative properties of the slice filtration. PhD thesis, arXiv:0806.1704.Google Scholar
11.Spitzweck, Markus. Relations between slices and quotients of the algebraic cobordism spectrum. arXiv:0812.0749, to appear in HHA.Google Scholar
12.Spitzweck, Markus and Østvær, Paul Arne. The Bott inverted infinite projective space is homotopy algebraic K-theory. Bull. Lond. Math. Soc. 41(2):281–292, 2009.CrossRefGoogle Scholar
13.Voevodsky, V.. On the zero slice of the sphere spectrum. Tr. Mat. Inst. Steklova 246(Algebr. Geom. Metody, Svyazi i Prilozh.):106–115, 2004.Google Scholar
14.Voevodsky, Vladimir. A1-homotopy theory. In Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), number Extra Vol. I, pages 579–604 (electronic), 1998.CrossRefGoogle Scholar
15.Voevodsky, Vladimir. Open problems in the motivic stable homotopy theory. I. In Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser. 3, pages 3–34. Int. Press, Somerville, MA, 2002.Google Scholar